From this archived thread, 

, it looks like the family mart is no longer there and looking at google maps, I don't see any parking referenced in the archived thread.    Does anyone know of a covered alternative to the international parking structure close to the airport?

I recently used the first one coming from road 402 turning left to the airport. I think it's 100 baht per day, covered, they provide transfer to and from the airport.

20 hours ago, stevenl said:

I recently used the first one coming from road 402 turning left to the airport. I think it's 100 baht per day, covered, they provide transfer to and from the airport.

The Mrs managed to find a place right after the domestic terminal before the cargo terminal.  I believe she said it's on the soi that has the 7/11 on it ( perhaps the 7/11 replaced the family mart)  It is 100 baht a day and covered.

As a follow up, this page has some more places listed.  https://airportplaces.com/phuket-international-airport-hkt/parking/

  

 

We parked at K Nin car park and they were prompt and waiting for us at the airport upon arrival. 100 baht a day for covered parking basically right across the street from the domestic terminal.